MinT - Information on Result #1106722

Information on Result #1106722

Linear OOA(256³⁷, 1677720, F₂₅₆, 5, 13) (dual of [(1677720, 5), 8388563, 14]-NRT-code), using OOA 5-folding based on linear OA(256³⁷, 8388600, F₂₅₆, 13) (dual of [8388600, 8388563, 14]-code), using

discarding factors / shortening the dual code based on linear OA(256³⁷, large, F₂₅₆, 13) (dual of [large, large−37, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(256³⁷, 1677720, F₂₅₆, 5, 12) (dual of [(1677720, 5), 8388563, 13]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(256⁴², 1677721, F₂₅₆, 5, 13) (dual of [(1677721, 5), 8388563, 14]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(256³⁸, 1677720, F₂₅₆, 5, 13) (dual of [(1677720, 5), 8388562, 14]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(256³⁹, 1677720, F₂₅₆, 5, 13) (dual of [(1677720, 5), 8388561, 14]-NRT-code)	[i]
5	Linear OOA(256⁴¹, 1677720, F₂₅₆, 5, 13) (dual of [(1677720, 5), 8388559, 14]-NRT-code)	[i]
6	Linear OOA(256⁴³, 1677977, F₂₅₆, 5, 13) (dual of [(1677977, 5), 8389842, 14]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
7	Linear OOA(256⁴⁴, 1677978, F₂₅₆, 5, 13) (dual of [(1677978, 5), 8389846, 14]-NRT-code)	[i]
8	Linear OOA(256⁴⁵, 1677979, F₂₅₆, 5, 13) (dual of [(1677979, 5), 8389850, 14]-NRT-code)	[i]
9	Linear OOA(256⁴⁶, 1678234, F₂₅₆, 5, 13) (dual of [(1678234, 5), 8391124, 14]-NRT-code)	[i]
10	Linear OOA(256⁴⁷, 1678235, F₂₅₆, 5, 13) (dual of [(1678235, 5), 8391128, 14]-NRT-code)	[i]
11	Linear OOA(256⁴⁸, 1699566, F₂₅₆, 5, 13) (dual of [(1699566, 5), 8497782, 14]-NRT-code)	[i]
12	Linear OOA(256⁴⁹, 1699567, F₂₅₆, 5, 13) (dual of [(1699567, 5), 8497786, 14]-NRT-code)	[i]
13	Linear OOA(256⁵⁰, 1699568, F₂₅₆, 5, 13) (dual of [(1699568, 5), 8497790, 14]-NRT-code)	[i]
14	Linear OOA(256⁵¹, 1743511, F₂₅₆, 5, 13) (dual of [(1743511, 5), 8717504, 14]-NRT-code)	[i]
15	Linear OOA(256⁵², 1743512, F₂₅₆, 5, 13) (dual of [(1743512, 5), 8717508, 14]-NRT-code)	[i]
16	Linear OOA(256⁵³, 3355440, F₂₅₆, 5, 13) (dual of [(3355440, 5), 16777147, 14]-NRT-code)	[i]
17	Linear OOA(256⁵¹, 1743512, F₂₅₆, 5, 13) (dual of [(1743512, 5), 8717509, 14]-NRT-code)	[i]
18	Linear OOA(256⁵², 1743513, F₂₅₆, 5, 13) (dual of [(1743513, 5), 8717513, 14]-NRT-code)	[i]
19	Linear OOA(256⁶⁸, 5033674, F₂₅₆, 5, 13) (dual of [(5033674, 5), 25168302, 14]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
20	Linear OOA(256⁶², 3388337, F₂₅₆, 5, 13) (dual of [(3388337, 5), 16941623, 14]-NRT-code)	[i]
21	Linear OOA(256⁶⁶, 5033417, F₂₅₆, 5, 13) (dual of [(5033417, 5), 25167019, 14]-NRT-code)	[i]
22	Linear OOA(256⁶⁷, 5098697, F₂₅₆, 5, 13) (dual of [(5098697, 5), 25493418, 14]-NRT-code)	[i]
23	Linear OOA(256⁶⁸, 5164497, F₂₅₆, 5, 13) (dual of [(5164497, 5), 25822417, 14]-NRT-code)	[i]
24	Linear OOA(256⁵⁷, 3355697, F₂₅₆, 5, 13) (dual of [(3355697, 5), 16778428, 14]-NRT-code)	[i]
25	Linear OOA(256⁵⁸, 3355698, F₂₅₆, 5, 13) (dual of [(3355698, 5), 16778432, 14]-NRT-code)	[i]
26	Linear OOA(256⁵⁹, 3388080, F₂₅₆, 5, 13) (dual of [(3388080, 5), 16940341, 14]-NRT-code)	[i]
27	Linear OOA(256⁶⁰, 3388209, F₂₅₆, 5, 13) (dual of [(3388209, 5), 16940985, 14]-NRT-code)	[i]
28	Linear OOA(256⁶¹, 3421232, F₂₅₆, 5, 13) (dual of [(3421232, 5), 17106099, 14]-NRT-code)	[i]
29	Linear OOA(256⁶², 3421233, F₂₅₆, 5, 13) (dual of [(3421233, 5), 17106103, 14]-NRT-code)	[i]
30	Linear OOA(256⁶³, 5033160, F₂₅₆, 5, 13) (dual of [(5033160, 5), 25165737, 14]-NRT-code)	[i]